MHB How Do Vieta's Formulas Apply to Cubic Polynomial Roots?

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Vieta's formulas provide relationships between the coefficients of a cubic polynomial and its roots, allowing for the calculation of sums and products of the roots. The expressions for the sums of pairs of roots, such as $(\alpha+\beta)+(\alpha+\gamma)+(\beta+\gamma)$, can be derived using these formulas. Additionally, the product of sums of pairs of roots, represented by $(\alpha+\beta)(\alpha+\gamma)(\beta+\gamma)$, can also be evaluated through Vieta's relationships. Another expression, $(\alpha+\beta)(\alpha+\gamma)+(\beta+\gamma)(\alpha + \beta)+(\alpha+\gamma)(\beta+\gamma)$, showcases further applications of Vieta's formulas in understanding cubic polynomials. Overall, these discussions highlight the utility of Vieta's formulas in analyzing the relationships between roots of cubic polynomials.
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You can read $\alpha + \beta + \gamma $, $\alpha\beta +\alpha \gamma + \beta \gamma$ and $\alpha \beta \gamma$ off from the polynomial.

Now what's $(\alpha+\beta)+(\alpha+\gamma)+(\beta+\gamma)$?

And what's $(\alpha+\beta)(\alpha+\gamma)(\beta+\gamma)$?

And finally $(\alpha+\beta)(\alpha+\gamma)+(\beta+\gamma)(\alpha + \beta)+(\alpha+\gamma)(\beta+\gamma)$?Those questions all seem to be an exercise in Vietas formulas.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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